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A178143
Sum of squares d^2 over the divisors d=2 and/or d=3 of n.
3
0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4
OFFSET
1,2
COMMENTS
Period 6: repeat [0, 4, 9, 4, 0, 13]. - Wesley Ivan Hurt, Jul 05 2016
FORMULA
a(n) = Sum_{d|n, d=2 and/or d=3} d^2.
a(n) = -a(n-1) + a(n-3) + a(n-4) for n>4.
G.f.: x*(4+13*x+13*x^2) / ( (1-x)*(1+x)*(1+x+x^2) ).
a(n+6) = a(n).
a(n) = A010675(n) + A021115(n). [R. J. Mathar, May 28 2010]
a(n) = 4 * (1 + floor(n/2) - ceiling(n/2)) + 9 * (1 + floor(n/3) - ceiling(n/3)). - Wesley Ivan Hurt, May 20 2013
a(n) = 5 + 2*cos(n*Pi) + 6*cos(2*n*Pi/3). - Wesley Ivan Hurt, Jul 05 2016
EXAMPLE
a(1)=0, a(2)=2^2=4 since 2|2, a(3)=3^2=9 since 3|3, a(4)=2^2=4 since 2|4.
MAPLE
seq(op([0, 4, 9, 4, 0, 13]), n=1..30); # Wesley Ivan Hurt, Jul 05 2016
MATHEMATICA
PadRight[{}, 100, {0, 4, 9, 4, 0, 13}] (* Wesley Ivan Hurt, Jul 05 2016 *)
PROG
(PARI) a(n)=[13, 0, 4, 9, 4, 0][n%6+1] \\ Charles R Greathouse IV, May 21 2013
(Magma) &cat [[0, 4, 9, 4, 0, 13]^^20]; // Wesley Ivan Hurt, Jul 05 2016
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Vladimir Shevelev, May 21 2010
EXTENSIONS
Replaced recurrence by a shorter one; added keyword:less - R. J. Mathar, May 28 2010
STATUS
approved